Download WOSMS8TH GRADE MATH 2011 - 2012 3rd 6 Weeks November 14

8TH GRADE MATH
WOSMS
3rd 6 Weeks
November 14 – January 20
29 days
TEKS
8.4A
Generate a different
representation of data
given another
representation of data
(such as a table, graph,
equation, or verbal
description).
8.5A
Predict, find, and justify
solutions to application
problems using
appropriate tables, graphs,
and algebraic equations.
8.5B
Find and evaluate an
algebraic expression to
determine any term in an
arithmetic sequence (with
a constant rate of change).
8.14A
Identify and apply
mathematics to everyday
experiences, to activities in
and outside of school, with
other disciplines, and with
other mathematical topics.
1
Objective
Days
2,6
7
Instructional Scope
Connect a model of an arithmetic
sequence to its algebraic
representation.


Include situations that connect to
everyday activities and with other
mathematical topics.
Predict a rule for a model and
justify the answer.
Example:
Nicole built the following figures using
color tiles.
Figure 1
Figure 2
Figure 3
What rule do you think Nicole is using?
Justify your answer. (A student may
incorrectly answer that the rule is n + 1
since each figure increases by 1. The
rule is n + 2.)
 Encourage students to write a
verbal description of the model that
relates the figure number to the
model.
2011 - 2012
Instruction
Resources
TAKS Mathematics
Preparation Grade 8
(Region 4) “Patterns
and Sequence
Lesson.”
Assessment
TAKS Mathematics
Preparation Grade 8
(Region 4) “Objective 2
Selected Response
Questions,” 9, 10.
www.mathbenchmarks.org
Rethinking Middle
School
Mathematics:
Geometry Across
the TEKS
(TEXTEAMS)
“Tricky Trapezoids.”
8TH GRADE MATH
WOSMS
8.14B
Use a problem-solving
model that incorporates
understanding the
problem, making a plan,
carrying out the plan, and
evaluating the solution for
reasonableness.
8.15A
Communicate
mathematical ideas using
language, efficient tools,
appropriate units, and
graphical, numerical,
physical, or algebraic
mathematical models.
8.16A
Make conjectures from
patterns or sets of
examples and
nonexamples.
8.16B
Validate his/her
conclusions using
mathematical properties
and relationships.
2
2011 - 2012
Example:
Write a verbal description that
relates the figure number to the
area of the figures shown below.
Figure 1
Figure 2
Figure 3
(There are always two tiles on the
base of the figure. The remaining
tiles are the same as the figure
number.)

Encourage students to build tables
that include a process column to
determine the relationship between
the figure number and its value.
Example:
Write an algebraic expression that
will find the area of the nth figure
where n represents the figure
number. Justify your answer.
Figure
Number
Process
Column
Area
1
1+2
3
2
2+2
4
3
3+2
5
n
n+2
8TH GRADE MATH
WOSMS
2011 - 2012
Using the above figures, what will
be the area of the 20th figure?
Justify your answer. (22)
What is the figure number of a
figure that has an area of 46?
Justify your answer. (44)
8.4A
Generate a different
representation of data
given another
representation of data
(such as a table, graph,
equation, or verbal
description).
8.5A
Predict, find, and justify
solutions to application
problems using
appropriate tables, graphs,
and algebraic equations.
8.5B
Find and evaluate an
algebraic expression to
determine any term in an
arithmetic sequence (with
a constant rate of change).
8.14A
Identify and apply
mathematics to everyday
experiences, to activities in
and outside of school, with
other disciplines, and with
other mathematical topics.
3
2,6
3
Use an algebraic expression to find
any term in an arithmetic sequence.

Encourage students to build tables
that include a process column to
determine the relationship between
the position of a term in a
sequence and the value of the
term.
o
Include selected response
items to determine if students
are connecting the relationship
between the position of the
term (figure number, etc.) and
its value (or area, etc.).
Example: Write an expression that
can be used to find the value of the
term in the nth position for the
sequence below. (0.5n)
Position in
Sequence
1
2
3
n
Term
0.5
1
1.5
?
www.mathbenchmarks.org
8TH GRADE MATH
WOSMS
8.14B
Use a problem-solving
model that incorporates
understanding the
problem, making a plan,
carrying out the plan, and
evaluating the solution for
reasonableness.
2011 - 2012
Example: The expression shown
below describes a pattern of
numbers.
3(n  4 )  7
If n represents a number’s position
in the sequence, find the first four
numbers in this sequence.
Possible solution:
Position
Process
Value
1
3(1 + 4) – 7
8
2
3(2 + 4) – 7
11
3
3(3 + 4) – 7
14
Example: Let n represent the
position
number
in 7the 17
4 of a 3(4
+ 4) –
following arithmetic sequence.
(8, 11, 14,317) 9
, 3, , 6, ...
2
2
Determine the expression that can
be used to find any term in this
sequence.
Possible solution:
Position
Process
Value
1
1
3
2
3
2
2
2
3
2
3
3
3
3
2
9
2
4
4
3
2
6
n
3
2
4
8TH GRADE MATH
WOSMS
2011 - 2012
 3
3 
 n  2  or  n 


2 
Example: The expression shown
below describes a pattern of
numbers.
3(n  4 )  7
If n represents a number’s position
in the sequence, find the first four
numbers in this sequence.
Possible solution:
Position
Process
Value
1
3(1 + 4) – 7
8
2
3(2 + 4) – 7
11
3
3(3 + 4) – 7
14
Example: Let n represent the
position
4 of a 3(4
number
+ 4) –
in 7the 17
following arithmetic sequence.
(8, 11, 14,317) 9
, 3, , 6, ...
2
2
Determine the expression that can
be used to find any term in this
sequence.
5
8TH GRADE MATH
WOSMS
2011 - 2012
Possible solution:
Position
Process
1
1
3
2
3
2
2
2
3
2
3
3
3
3
2
9
2
3
 34
 3 4  2
or
n

 2
 2 n




8.4A
Generate a different
representation of data
given another
representation of data
(such as a table, graph,
equation, or verbal
description).
8.5A
Predict, find and justify
solutions to application
problems using
appropriate tables, graphs,
and algebraic equations.
8.14A
Identify and apply
mathematics to everyday
experiences, to activities in
and outside of school, with
other disciplines, and with
other mathematical topics.
6
2,6
7
Value
n
6
3
2
Generate different representations
of
data.




Include situations that connect to
everyday activities and with other
mathematical topics.
Use data from a verbal description
to generate a table, a graph, and
an equation.
o Include making predictions
concerning the graph of the
data.
Use data from a table to generate a
verbal description, a table, and an
equation.
Use data from a graph to generate
a verbal description, a table, and
an equation.
Rethinking Middle
School
Mathematics:
Proportionality
Across the TEKS
(TEXTEAMS) “Jet
Ski Rental.”
TAKS Mathematics
Preparation Grade 8
(Region 4) “Objective 2
Selected Response
Questions,” 7, 8.
www.mathbenchmarks.org
8TH GRADE MATH
WOSMS
8.14B
Use a problem-solving
model that incorporates
understanding the
problem, making a plan,
carrying out the plan, and
evaluating the solution for
reasonableness.
8.15A
Communicate
mathematical ideas using
language, efficient tools,
appropriate units, and
graphical, numerical,
physical, or algebraic
mathematical models.
8.16B
Validate his/her
conclusions using
mathematical properties
and relationships.
7
The following example could be
given to students as the verbal
description, data table, graph, or
equation. Students would then
provide the other representations.
Example:
Yan works in the concession stand
at the ballpark and earns $4.00 per
hour.
Complete a table that shows the
relationship between y, the amount
of money Yan earns for every x
hour worked.
Hours
Worked
(x)
Process
Column
Money
Earned
(y)
1
$4.00
2
$8.00
3
($12.00)
4
($16.00)
8
($32.00)
12
($48.00)
20
($80.00)
x
($4.00x)
2011 - 2012
WOSMS
8TH GRADE MATH
Write a sentence that describes the
relationship between the amount of
money earned and the number of
hours worked. (The amount of
money earned is 4 times the
number of hours worked.)
Write an equation that can be used
to determine x, the number of hours
worked to earn $150.00. (4x = 150)
Predict what the graph of the data
will look like. (Answers may vary.)
Graph the data.
What does the ordered pair
(3.5, 14) mean? (Yan worked 3.5
hours and earned $14.00.)
How much money will Yan earn if
she works 15 hours in one week?
Justify your answer. ($60)
Yan is saving her earnings to buy
8
2011 - 2012
8TH GRADE MATH
WOSMS
2011 - 2012
her mother a birthday gift. If the gift
costs $75.00, how many hours
must she work? Justify your
answer. (19 hours)
Yan received a raise and now earns
$5.00 per hour. How will this affect the
graph of her earnings? (The graph will
be steeper.)
8.5A
Predict, find and justify
solutions to application
problems using
appropriate tables, graphs,
and algebraic equations.
8.14D
Select tools such as real
objects, manipulatives,
paper/pencil, and
technology or techniques
such as mental math,
estimation, and number
sense to solve problems.
8.15A
Communicate
mathematical ideas using
language, efficient tools,
appropriate units, and
graphical, numerical,
physical, or algebraic
mathematical models.
2,6
7
Solve equations that arise from
problem situations.



Have students match a given
equation with different data tables
and/or different graphs.
Have students justify the solution.


9
Solve one-step and two-step
equations.
o Estimate solutions.
o Determine the exact solution
(using concrete models if
necessary).
o Justify the solution.
Estimate and justify solutions.
Match equations to solution
strategies.
Use an equation to generate a
problem situation and related data
with a verbal description, a table,
and a graph.
Have students create a scenario, a
data table, and a graph for a given
Rethinking Middle
School
Mathematics:
Algebraic
Reasoning Across
the TEKS
(TEXTEAMS)
“Cross-Country
Cycling.”
Rethinking Middle
School
Mathematics:
Algebraic
Reasoning Across
the TEKS
(TEXTEAMS)
“Making
Connections
Activities 3 and 4.”
www.mathbenchmarks.org
8TH GRADE MATH
WOSMS
8.15B
Evaluate the effectiveness
of different representations
to communicate ideas.

8.16A
Make conjectures from
patterns or sets of
examples and
nonexamples.
8.16B
Validate his/her
conclusions using
mathematical properties
and relationships.
8.4A
Generate a different
representation of data
given another
representation of data
(such as a table, graph,
equation, or verbal
description).
2,3,6
5
equation. Have students justify the
solution.
Solve problems using tables,
graphs, and equations.
o
Estimate solutions.
o Justify the solution
Graph translations and reflections.


Predict placement before graphing.
Determine how an ordered pair
changes under a specific
translation or reflection (under a
given rule).
Example: If point A (–3, 2) is
8.6B
Graph dilations,
reflections, and
translations on a
coordinate plane.
translated under the rule (x – 5, y),
what will be the new coordinates of
point A? Justify your answer.
8.7D
Locate and name points
on a coordinate plane
using ordered pairs of
rational numbers.
(–8, 2)
Example: If point B (5, –7) is
8.14D
Select tools such as real
objects, manipulatives,
10
reflected across the y-axis, what
2011 - 2012
Rethinking Middle
School
Mathematics:
Algebraic
Reasoning Across
the TEKS
(TEXTEAMS)
“Cover Up.”
TAKS Mathematics
Preparation Grade 8
(Region 4)
“Coordinate
Translation Lesson.”
TAKS Mathematics
Preparation Grade 8
(Region 4) “Objective 3
Selected Response
Questions,” 4.
TAKS Mathematics
Preparation Grade 8
(Region 4)
“Coordinate
Reflection Lesson.”
www.mathbenchmarks.org
Rethinking Middle
School
Mathematics:
Geometry Across
the TEKS
(TEXTEAMS)
“Translations.”
8TH GRADE MATH
WOSMS
will be the coordinates of B ?
paper/pencil, and
technology or techniques
such as mental math,
estimation, and number
sense to solve problems.
(–5, –7)

8.16A
Make conjectures from
patterns or sets of
examples and
nonexamples.
8.7D
Locate and name points
on a coordinate plane
using ordered pairs of
rational numbers.
11
Rethinking Middle
School
Mathematics:
Geometry Across
the TEKS
(TEXTEAMS)
“Reflections.”
Example: What rule describes the
translation of ABC to AB C  ?
Justify your answer. (x + 8, y – 5)

8.6B
Graph dilations,
reflections, and
translations on a
coordinate plane.
Determine the relationship (or rule)
between given ordered pairs of the
original image and the reflected or
translated image.
2011 - 2012
3,6
8
Evaluate reasonableness of
solutions.
Graph the dilations on a coordinate
plane (include rational numbers).


Graph dilations (enlargements and
reductions) on a coordinate plane.
Determine the scale factor of a
dilation given the original figure and
the dilated figure on a coordinate
plane.
TAKS Mathematics
Preparation Grade 8
(Region 4)
“Coordinate Dilation
Lesson.”
TAKS Mathematics
Preparation Grade 8
(Region 4) “Objective 3
Selected Response
Questions,” 1, 2, 3.
www.mathbenchmarks.org
8TH GRADE MATH
WOSMS
Example: Triangle ABC was dilated to
form triangle DEF.
8.14A
Identify and apply
mathematics to everyday
experiences, to activities in
and outside of school, with
other disciplines, and with
other mathematical topics.
8.14B
Use a problem-solving
model that incorporates
understanding the
problem, making a plan,
carrying out the plan, and
evaluating the solution for
reasonableness.
8.15A
Communicate
mathematical ideas using
language, efficient tools,
appropriate units, and
graphical, numerical,
physical, or algebraic
mathematical models.
12
What number represents the scale
factor used to change triangle ABC
into triangle DEF? Justify your
answer. (The scale factor is 2.

Determine the relationship (rule)
between given ordered pairs of the
original image and the dilated
image. (Students should be able to
explain the presence of the scale
factor in the rule
(scale factor  x, scale factor  y ) .)

Evaluate reasonableness.
2011 - 2012